Why Investigate Root Architecture and Water Uptake?

• Spatially variable models are needed as precision agriculture takes hold. (Steve R. Green 2006)
• 3D models coupling soil waterflow and root uptake could be used to test hypotheses of root permeability, architecture adapatiation, and genotypic affects on uptake and solute transport. (Sophie de Dorlodot and Draye 2007)

Theory & History

• Root-Soil Water Movement and Solue Model (R-SWMS)
  • Coupling of two models: one focused on whole root system continuinty (F. Somma and Clausnitzer 1998) and one focused on (Claude Doussan and Vercambre 1998)
• Richard’s Equation
• One-Dimensional vs Two-Dimensional vs Three-Dimensional
  • Processing power: How many parameters is too many?
• 3D models can tackle some major issues:
  • Different roots have different funcitons.
  • Soil water content is heterogeneous.
  • Water uptake is a passive process

Root-Soil Water Movement and Solute Model (R-SWMS)

• The root-soil water movement and solute model is used to describe the flow of water and nutrients based on gradients towards the root collar.

Richard’s Equation

• The equation is used to describe water flow?

• \(\frac{\partial \theta}{\partial t} = \nabla \cdot [\textbf{K} \nabla(h-z)] - S\)
  
  
  • \(\theta =\) volumetric water content
  • \(t =\) time
  • \(\textbf{K} =\) hydraulic conductivity tensor
  • \(h =\) water pontential on a weight basis
  • \(S =\) sink term representing root water uptake
  • \(z =\) vertical coordinate

Solving Richard’s Equation

• Radial Flow (Soil-Root):
  • \(J_{r} = K_{r}^{*}s_{r}[h_{s}(z)-h_{x}(z)]\)
• Axial Flow (Xylem):
  • \(J_{x} = -K_{x}(\frac{\Delta h_{x}}{l} + \frac{\Delta z}{l})\)
    
    
    • \(K_{r}^{*} =\) intrinsic radial conductivity
    • \(K_{x} =\) xylem conductivity
    • \(h_{s} =\) water potential at the root surface
    • \(h_{x} =\) water potential in the xylem
    • \(s_{r} =\) outer surface of the root segment
    • \(l =\) length of the root segment
    • \(z =\) vertical coordinate

Solving Richard’s Equation Cont.

• \(S_{j} = \frac{\sum\limits_{i}^{n_{i}}{J_{r,i}}}{V_{j}}\)
  
  
  • \(V_{j} =\) voxel volume: going to be \(1 \ cm^3\)
  • \(n_{i} =\) number of root segments within voxel j

Assumptions

• What are the assumptions?
• Soil water is preferably taken up at spatial locations where the energy to bring water to the root collar is minimized.
• Osmotic potential is negligible and root water capacity can be neglected.
  • Valid under normal conditions. What about water stress?

The Questions

Methodology

• Colar Boundary Conditions (CBCs)

• Input reference and varied paramters

Methodology Cont.

Results

Results Cont.

More Results

More Results Cont.

Even More Results

Even More Results Cont.

But Wait… There’s More

But Wait… There’s More Cont.

BUT WAAAAIT! THERE’S MORE!

BUT WAAAAIT! THERE’S MORE! Cont.

Okay Really?

Okay Really? Cont.

Finally…

Conclusions

• Well finally…

Images and Movies

• Click ‘P’

LaTex Equations

1. \(y = \beta_1 + \beta_2 x + \varepsilon_1\)
2. \(\mu = \displaystyle \frac{\sum\limits_{i=0}^n{x_i}}{n}\)
3. Miscellanious stuff
   1. \(\sqrt{x} \quad \displaystyle \binom{k}{n} \quad \frac{\partial f}{\partial x}\)
   2. \(A \cup B \qquad A \cap B \qquad A \in B\)
   3. \(\Delta \verb/ or / \delta ?\)
   4. \(\displaystyle \int_0^{\infty} f(x) \quad \displaystyle \lim_{x\to\infty}\)
      
      
      1. Wow. Look at all that LaTex

References